What is ln((\sqrt[3]{5})/(25)) ?

The solution to ln((\sqrt[3]{5})/(25)) is -5/3 ln(5)

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simplify ln((\sqrt[3]{5})/(25))

simplify

- \frac{5}{3} ln (5)

Decimal Notation

- 2.68239 \dots

Solution steps

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

= \frac{1}{3} ln (5) - ln (25)

ln (25) = 2 ln (5)

= \frac{1}{3} ln (5) - 2 ln (5)

Factor out common term

ln (5)

= ln (5) (\frac{1}{3} - 2)

\frac{1}{3} - 2 = - \frac{5}{3}

= - \frac{5}{3} ln (5)

lo g_{10} (z^{5} y)

lo g_{10} (x^{7} y)

- ln (3.02 \cdot 1 0^{- 8})

ln (3) - ln (10)

10 ln (\frac{i ( t )}{2})

What is ln((\sqrt[3]{5})/(25)) ?
The solution to ln((\sqrt[3]{5})/(25)) is -5/3 ln(5)